1. Following what we did in equations (2.14) to (2.17), show that the direct product of a vector and a 3rd-rank tensor is a 4th-rank tensor. Also show that the direct product of two 2nd-rank tensors is a 4th-rank tensor. Generalize this to show that the direct product of two tensors of ranks m and n is a tensor of rank m + n.
1. Following what we did in equations (2.14) to (2.17), show that the direct product of a vector and a 3rd-rank tensor is a 4th-rank tensor. Also show that the direct product of two 2nd-rank tensors is a 4th-rank tensor. Generalize this to show that the direct product of two tensors of ranks m and n is a tensor of rank m + n.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 44E
Related questions
Question
Subject : Mathematical Physics 2
Topic: Tensor Analysis
Please answer it in full details and show your solutions clearly.
![1. Following what we did in equations (2.14) to (2.17), show that the direct product of a vector
and a 3rd-rank tensor is a 4th-rank tensor. Also show that the direct product of two 2nd-rank tensors
is a 4th-rank tensor. Generalize this to show that the direct product of two tensors of ranks m and
n is a tensor of rank m + n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F186f3b4d-0711-4b68-af8c-77b6a691068b%2Fd981cbf5-1cff-465f-8b65-99cd172982eb%2F739xdvf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Following what we did in equations (2.14) to (2.17), show that the direct product of a vector
and a 3rd-rank tensor is a 4th-rank tensor. Also show that the direct product of two 2nd-rank tensors
is a 4th-rank tensor. Generalize this to show that the direct product of two tensors of ranks m and
n is a tensor of rank m + n.
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